This paper presents a comprehensive review of the design and implementation methods of low-power piezoelectric energy harvesting circuits, which in the last few years have gained an extremely large range of applications like the power sources of wearable electronic devices, such as biometrical sensors. Before examining the electronic circuitries of the self-supplied power devices, an overview of the structure, equivalent electrical circuits, and basic parameters of the piezoelectric generators and MEMSs as energy harvesting elements is presented. The structure of energy storage elements (parallel-plate capacitors and thin-film supercapacitors), suitable for this type of application, is also presented. The description of these components from an electrical point of view allows them to be easily workable when connected to the various power conversion electronic circuits. Based on an overview of the structure and the principles of operation, as well as some analytical expressions for energy efficiency evaluation, a comprehensive comparative analysis is presented. Depending on the advantages and disadvantages of the known circuit configurations, the basic electrical and design parameters are systematized in tabular form. Practical realizations of piezoelectric power conversion circuits are also presented in graphic form, ensuring the optimal value of energy efficiency and compactness in the construction of the devices.